Question

If `5/(a-b) = 2` and if `a=4`, what is the value of `b`?

Answer 1

To solve this we must substitute `color(red)(4)` for `color(red)(a)` in the expression and then solve for `b`:

`5/(color(red)(a) - b) = 2` becomes:

`5/(color(red)(4) - b) = 2`

`5/(4 - b) xx color(red)((4 - b)) = 2color(red)((4 - b))`

`5/color(red)(cancel(color(black)(4 - b))) xx cancel(color(red)((4 - b))) = (2 xx 4) - (2 xx b)`

`5 = 8 - 2b`

`5 - color(red)(8) = -color(red)(8) + 8 - 2b`

`-3 = 0 - 2b`

`-3 = -2b`

`(-3)/color(red)(-2) = (-2b)/color(red)(-2)`

`3/2 = (color(red)(cancel(color(black)(-2)))b)/cancel(color(red)(-2))`

`3/2 = b`

`b = 3/2`